Clustering illusion

Up to 10,000 points randomly distributed inside a square with apparent "clumps" or clusters

The clustering illusion is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of variability likely to appear in a small sample of random or semi-random data.[1]

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Thomas Gilovich, an early author on the subject, argued that the effect occurs for different types of random dispersions, including two-dimensional data such as clusters in the locations of impact of World War IIV-1 flying bombs on maps of London; or seeing patterns in stock market price fluctuations over time.[1][2] Although Londoners developed specific theories about the pattern of impacts within London, a statistical analysis by R. D. Clarke originally published in 1946 showed that the impacts of V-2 rockets on London were a close fit to a random distribution.[3][4][5][6][7]

The clustering illusion is central to the "hot hand fallacy", the first study of which was reported by Gilovich, Robert Vallone and Amos Tversky. They found that the idea that basketball players shoot successfully in "streaks", sometimes referred to by sportcasters as having a "hot hand" and widely believed by Gilovich et al.'s subjects, was false. In the data they collected, if anything the success of a previous throw very slightly predicted a subsequent miss rather than another success.[8]